| Could be a number of things, as Tim and Gary say above.
One thing though, especially seeing as it's becoming an issue for you, is tension. When you get tense you grab the bars, it's a survival reaction. I wouldn't mind betting that you're hanging on to the bars a bit tight, weighting the inside bar and/or not relaxing after the push. Remember there's two steps to the counter steer, a push and a relax. The bike will settle into it's own line if you have no input into the bike so it stands to reason that you are forcing the bike to do something it doesn't want to do.
The only way to really find out what is happening is to have someone following you when you try the quick turn to see what is happening. In the meantime - try practising the quick turn and making a conscious effort to relax. Even go so far as to flap your arms before and after - it might look and feel stupid but it's a good physical reminder for you and will help you relax. | 
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